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MLPG approximation to the p-Laplace problem

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Abstract

Meshless local Petrov-Galerkin (MLPG) method is discussed for solving 2D, nonlinear, elliptic p-Laplace or p-harmonic equation in this article. The problem is transferred to corresponding local boundary integral equation (LBIE) using Divergence theorem. The analyzed domain is divided into small circular sub-domains to which the LBIE is applied. To approximate the unknown physical quantities, nodal points spread over the analyzed domain and MLS approximation, are utilized. The method is a meshless method, since it does not require any background interpolation and integration cells and it dose not depend on geometry of domain. The proposed scheme is simple and computationally attractive. Applications are demonstrated through illustrative examples.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran

    Davoud Mirzaei & Mehdi Dehghan

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  1. Davoud Mirzaei
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  2. Mehdi Dehghan
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Correspondence to Mehdi Dehghan.

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Mirzaei, D., Dehghan, M. MLPG approximation to the p-Laplace problem. Comput Mech 46, 805–812 (2010). https://doi.org/10.1007/s00466-010-0521-1

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  • DOI: https://doi.org/10.1007/s00466-010-0521-1

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